The specific play seen in Scream 2 is "Agamemnon", and it can be identified because Cassandra and the chorous are wondering if she should enter the palace, since she knows she will die if doing so.
Sidney Prescott landed the leading role as Cassandra and was nervous about performing due to the murders. However, her drama professor understood and Sidney decided to do so anyway. During rehearsal for the play, a scene from after the fall of Troy., Ghostface, wearing a brown cloak just as the chorus is wearing, arrives and attacks Sidney during a scene of mass chaos where the chorous is running around chasing her with fake daggers. Sidney finally collapses and screams, although it is not clear if this is simply a figment of Sidney's imagination or not. If Ghostface really did attack, it is likely that the killer was Mickey, since he was in the area at the time. Mostlikely Sidney did not imagine the attack, because you can see Ghostface run away.
Later in the film, Sidney uses props from the play to her advantage, using the pillars to knock down Mrs. Loomis. This is foreshadowed during the original play scene when you can see falling bricks from the unstable set.
SignifiganceCoincidentally, The Oresteia is a trilogy that appears in the second installment of the Scream franchise, which would later become a trilogy of its own in 2000.
Another interesting note is that The Oresteia is a tragedy focusing around a single female heroine, Cassandra. The Scream trilogy is also a tragedy focusing around a single female heroine, Sidney Prescott. The Oresteia is about Cassandra's life after she is cursed by Apollo. The Scream franchise is about Sidney's life after her mother's death, which can be considered a "curse" as it sets in motion the tragic events of the entire series.
A running theme in this play trilogy is murder and revenge. Clytemnestra kills Agamemnon for sacrificing their daughter and having an affair, and Orestes, their son, seeks revenge for his father's death and mother's affair by killing Clytemnestra, his mother. In this movie, Mrs. Loomis is seeking revenge from Sidney for the death of her son, who killed Sidney's mother for having an affair with his father. The climax of this film about familial murder and revenge plays out on the set of the play about familial murder and revenge.